1. ### Different Approaches to Solution of The Assignment Problem Using R Program

Öznur İşçi Güneri, Burcu Durmuş, Dursun Aydın

Department of Statistics, Muğla Sıtkı Koçman University, Kötekli Campus, 48000, Muğla, Turkey.

Abstract: The aim of the current study is to emphasize the importance of an heuristic solution method for the classical assignment problem (AP). In the literature, many different algorithms including both classical and heuristic algorithms have been developed to solve AP. In this study, we introduce newly R program codes for the classical and heuristic algorithms. Note that Brute Force algorithm, Hungarian algorithm, and Linear Programming (LP) algorithm are konown as classical algorithms, while the Greedy is considered as the heuristic algorithm. For this purpose, we made an application based on 4×4 dimensional sample. In addition, four different methods are obtained for different dimensional problems. The outcomes from the study show that both classical methods and the Greedy method provides the optimal or near optimal results.

Keywords: Assignment Problem, Linear Programming (LP), Brute Force Method, Hungarian Algorithm, Greedy Method.

2. ### Deriving, and Learning About, Spatial Demand Distributions in Location Models

Yigal Gerchak

Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel.

Abstract: Location models typically assume that the spatial demand distribution or weights of demand clusters is/are given. However, when a service is new, or considerably altered, such distributions are, in fact, learned gradually as more demands are realized. Recently, location analysts proposed robust optimization models which deal with ranges of weights. We argue that, in principle, uncertain weights can be viewed as mixtures of distributions, and are thus similar to ordinary weights. However, location analysts need a procedure, hopefully a simple one, to revise spatial probability distributions as more information is obtained. We provide a Bayesian model which accomplishes that in a sensible manner. We then show that this theory-based model is, in fact, equivalent to a very simple “physical” mechanism. As the spatial demand distribution evolves with experience, the home bases of servers can be adjusted accordingly, if feasible and desirable.

Keywords: Location, Learning, Bayesian, Robust Optimization.